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2 years ago

Which value would be a solution for x in the inequality 47-4x<7

Mathematics

1 answer:

cluponka [151]2 years ago

5 0

Answer:

x > 10

Step-by-step explanation:

47-4x<7

Subtract 47 from each side

47-47-4x<7-47

-4x < -40

Divide by -4. When dividing by a negative, flip the inequality.

-4x/-4 > -40/-4

x > 10

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Simplify for a = 3, b= -4 and c=-1. 16a - 3c + 5b =

-Dominant- [34]

Answer:

Step-by-step explanation:

16(3)-3(-1)+5(-4)

48+3-20

51-21

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3 years ago

Find the distance from point B to point C. Enter as a decimal rounded to the nearest tenth. BC = [?] mi

mina [271]

Answer: 0.0987987889 mi

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2 years ago

Solve for the unknown in the following diagram. Round the answer to two decimal places. in

Alexxandr [17]

Answer:

172.27 in

Step-by-step explanation:

Apply the Sine Rule

Sine Rule is given as:

$\frac{a}{sin(A)} = \frac{b}{sin(B)} = \frac{c}{sin(C)}$

c = x = ?

C = 180 - (52 + 48) = 80° (sum of triangle)

b = 130 in.

B = 48°

Plug in the values

$\frac{130}{sin(48)} = \frac{x}{sin(80)}$

Multiply both sides by sin(80)

$\frac{130*sin(80)}{sin(48)} = x$

172.274641 = x

x = 172.27 in. (to 2 decimal places)

4 0

2 years ago

Suppose h(x)=3x-2 and j(x) = ax +b. Find a relationship between a and b such that h(j(x)) = j(h(x))

sergejj [24]

Answer:

$\displaystyle a = \frac{1}{3} \text{ and } b = \frac{2}{3}$

Step-by-step explanation:

We can use the definition of inverse functions. Recall that if two functions, f and g are inverses, then:

$\displaystyle f(g(x)) = g(f(x)) = x$

So, we can let j be the inverse function of h.

Function h is given by:

$\displaystyle h(x) = y = 3x-2$

Find its inverse. Flip variables:

$x = 3y - 2$

Solve for y. Add:

$\displaystyle x + 2 = 3y$

Hence:

$\displaystyle h^{-1}(x) = j(x) = \frac{x+2}{3} = \frac{1}{3} x + \frac{2}{3}$

Therefore, a = 1/3 and b = 2/3.

We can verify our solution:

$\displaystyle \begin{aligned} h(j(x)) &= h\left( \frac{1}{3} x + \frac{2}{3}\right) \\ \\ &= 3\left(\frac{1}{3}x + \frac{2}{3}\right) -2 \\ \\ &= (x + 2) -2 \\ \\ &= x \end{aligned}$

And:

$\displaystyle \begin{aligned} j(h(x)) &= j\left(3x-2\right) \\ \\ &= \frac{1}{3}\left( 3x-2\right)+\frac{2}{3} \\ \\ &=\left( x- \frac{2}{3}\right) + \frac{2}{3} \\ \\ &= x \stackrel{\checkmark}{=} x\end{aligned}$

3 0

2 years ago

Edwina made a circular hula hoop out of a piece of tubing 152 inches long by bending it into a circle and taping the ends togeth

juin [17]

This is equal tio the diameter of the circle formed:-

152 ins = circumference and this = pi * diameter

so the Answer is 152 / pi = 48.4 ins to nearest tenth

48 inches to nearest inch.

7 0

3 years ago